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Results (6 matches)

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Label Class Base field Conductor norm Rank Torsion CM Sato-Tate Regulator Period Leading coeff j-invariant Weierstrass coefficients Weierstrass equation
16.5-a1 16.5-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $18.47046131$ 0.559968109 \( -343 a + 1029 \) \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -2 a\) , \( -a\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a+1\right){x}^{2}-2a{x}-a$
16.5-a2 16.5-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $4.617615327$ 0.559968109 \( -2701312025 a + 6919553753 \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 7 a - 2\) , \( 5 a - 5\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(7a-2\right){x}+5a-5$
16.5-a3 16.5-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $18.47046131$ 0.559968109 \( -24225 a + 68453 \) \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 2 a + 3\) , \( 0\bigr] \) ${y}^2+\left(a+1\right){x}{y}={x}^{3}+a{x}^{2}+\left(2a+3\right){x}$
16.5-a4 16.5-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/2\Z\oplus\Z/4\Z$ $\mathrm{SU}(2)$ $1$ $36.94092262$ 0.559968109 \( 1995 a + 5021 \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 12 a - 22\) , \( -7 a + 26\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(12a-22\right){x}-7a+26$
16.5-a5 16.5-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/2\Z$ $\mathrm{SU}(2)$ $1$ $9.235230655$ 0.559968109 \( 7659605 a + 11960871 \) \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -a - 4\) , \( 5 a - 16\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-a-4\right){x}+5a-16$
16.5-a6 16.5-a \(\Q(\sqrt{17}) \) \( 2^{4} \) 0 $\Z/8\Z$ $\mathrm{SU}(2)$ $1$ $36.94092262$ 0.559968109 \( 21069823 a + 33751811 \) \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 127 a - 317\) , \( -1109 a + 2848\bigr] \) ${y}^2+\left(a+1\right){x}{y}+\left(a+1\right){y}={x}^{3}+\left(a+1\right){x}^{2}+\left(127a-317\right){x}-1109a+2848$
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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.